classmarkov - recurrent and transient classes of Markov matrix

Calling Sequence

[perm,rec,tr,indsRec,indsT]=classmarkov(M)

Parameters

• M : real N x N Markov matrix. Sum of entries in each row should add to one.
• perm : integer permutation vector.
• rec, tr : integer vector, number (number of states in each recurrent classes, number of transient states).
• indsRec,indsT : integer vectors. (Indexes of recurrent and transient states).

Description

Returns a permutation vector perm such that

M(perm,perm) = [M11 0 0 0 0   0]
               [0 M22 0 0     0]
               [0 0 M33       0]
               [      ...      ]
               [0 0       Mrr 0]
               [* *        *  Q]
   

Each Mii is a Markov matrix of dimension rec(i) i=1,..,r. Q is sub-Markov matrix of dimension tr. States 1 to sum(rec) are recurrent and states from r+1 to n are transient. One has perm=[indsRec,indsT] where indsRec is a vector of size sum(rec) and indsT is a vector of size tr.

Examples

//P has two recurrent classes (with 2 and 1 states) 2 transient states
P=genmarkov([2,1],2,'perm')
[perm,rec,tr,indsRec,indsT]=classmarkov(P);
P(perm,perm)
 

See Also

genmarkov  eigenmarkov